Effective interaction of electrons in quantum wells

Effects of electron-phonon interaction on the interaction between electrons in semiconductor quantum wells are considered. It is found that the direct Coulomb potential between electrons in a quantum well is smaller than that in bulk semicondutors. The antisymmetric modes of the confined bulk phonons and interface phonons have no contribution to the effective interaction of electrons. If a well is narrow enough, the effective interaction between electrons caused by interaction with interface phonons may exceed that by interaction with confined bulk phonons. In narrower wells the effective interaction potential of electrons produced by phonons is stronger, but decreases rapidly with increasing distance between electrons.     

Inter- and intra-subband relaxation of hot electrons in GaAs/AlGaAs quantum wells

In this work, we have studied the inter- and intra-subband scattering of hot electrons in quantum wells using the hot electron-neutral acceptor luminescence technique. We have observed direct evidence of the emission of confined optical phonons by hot electrons excited slightly above the n=2 subband in GaAs/Al_0.37Ga_0.63As quantum wells. Scattering rates of photoexcited electrons via inter- and intra-subband LO phonon emission were calculated based on the dielectric continuum model. We found that, for wide wells with the Al composition of our experiments, both the calculated and experimental results suggest that the scattering of the electrons is dominated by the confined LO phonon mode. In the calculations, scatterings among higher subbands are also dominated by the same type of phonon at well width of 10 nm.     

Intersubband relaxation of hot carriers in quantum well systems

We use an ensemble Monte Carlo simulation of coupled electrons, holes and nonequilibrium polar optical phonons in multiple quantum well systems to model the intersubband relaxation of hot carriers measured in ultra-fast optical experiments. We have investigated the effect of various models of confined photon modes on the energy relaxation and intersubband transition rate in single quantum well and coupled well systems. In particular, the symmetry of the atomic displacement with respect to the quantum well has a marked effect on the relative intersubband versus intrasubband scattering rates, depending on whether one considers electrostatic boundary conditions(slab modes) or mechanical boundary conditions(guided modes). In single quantum wells systems, the overall intersubband relaxation time is not found to be strongly dependent on the confined mode model used due to competing effects of hot phonons and the relative intrasubband scattering rates. For coupled well systems, the relaxation rate is much more dependent on the exact nature of the phonon amplitude. Large effects are found associated with localized AlAs interface modes which dominate the intersubband relaxation time.     

Pair scattering of electrons in edge channels of opposite chiralities in the presence of a disorder potential

The nonequilibrium transfer of the energy between electrons of counter-propagating quasi-one-dimensional systems has been perturbatively calculated for edge channels in a two-dimensional system in the integer quantum Hall effect. The processes involving two electrons that are allowed only in the system with disorder have been taken into account. Expressions for the cases of Coulomb scattering and transfer of nonequilibrium phonons have been obtained. The energy transferred per unit time has a quasi-threshold dependence on the degree of nonequilibrium of the hot channel. According to numerical estimates for electrons in GaAs, Coulomb scattering processes dominate in the energy transfer and the expected effect can be experimentally observed.     

Kinetic theory of semiconductor cascade laser based on quantum wells and wires

The paper presents a numerical solution of a system of nonlinear equations for the electron distribution functions in the upper and lower subbands between which lasing transitions occur and the number of nonequilibrium optical phonons in semiconducting cascade lasers based on quantum wells and wires. For the case of quantum wells, we propose an analytical solution of this system of equations, which is a generalization of the previously found solution [V. F. Elesin and Yu. V. Kopaev, Zh. éksp. Teor. Fiz. 108, 2186 (1995) [JETP 81, 1192 (1995)]; V. F. Elesin and Yu. V. Kopaev, Sol. St. Commun. 96, 897 (1995)] in a wider range of injection rates. The threshold injection rate can be significantly reduced owing to reabsorption and accumulation of nonequilibrium optical phonons, nonparabolicity of the subbands and different effective masses of electrons in different subbands. In the case of quantum wires, the threshold injection rate is considerably lower, and its decrease is even larger than in quantum wells. It is remarkable that, owing to the lower electron-electron relaxation rate in the one-dimensional case, the decrease in the threshold injection rate may be two or three orders of magnitude. The relation between the density of states and threshold current has also been studied. Zh. éksp. Teor. Fiz. 111, 681–695 (February 1997)     

Coherent state polarons in quantum wells

We investigate the polaronic effects of an electron confined in a quantum well, which we describe through its algebraic properties using su(1,1), taking into account the electron-bulk longitudinal-optical phonon interaction. We construct the variational wave function as the direct product of an electronic part and a part describing coherent phonons generated by the Low–Lee–Pines transformation from the vacuum state. We use two explicit forms of coherent states, Perelomov and Barut-Girardello states, to represent the electronic part in the quantum well spectrum. Our results show that in a coherent state basis for electrons the basic polaron parameters such as the energy gap shift and effective mass are further enhanced compared to those obtained with the conventional sinusoidal form of the basis. The difference between the two types of quantum well coherent states appears in polaronic interactions in quantum wells. We extend the calculations in order to estimate polaron lifetimes for a variety of different material systems.     

Heating and cooling of a two-dimensional electron gas by terahertz radiation

The absorption of terahertz radiation by free charge carriers in n-type semiconductor quantum wells accompanied by the interaction of electrons with acoustic and optical phonons is studied. It is shown that intrasubband optical transitions can cause both heating and cooling of the electron gas. The cooling of charge carriers occurs in a certain temperature and radiation frequency region where light is most efficiently absorbed due to intrasubband transitions with emission of optical phonons. In GaAs quantum wells, the optical cooling of electrons occurs most efficiently at liquid nitrogen temperatures, while cooling is possible even at room temperature in GaN heterostructures.     

Bound states of coupled plasmon-phonon modes at neutral donors in semiconductor quantum wells

The bound states of plasmons, of phonons and of coupled plasmon-phonon modes at neutral donors in semiconductor quantum well systems have been studied here. The interaction of plasmon-phonon excitations, which are important in compound semiconductor systems, with electrons, and the coupling of plasmons with electrons have been derived in the long wave length limit of the Random Phase approximation. These interactions are used to derive expressions for the binding energies of the collective excitations to neutral donors. The dependence of the binding energy of the coupled plasmon-phonon modes on the well width of quantum wells is found to be particularly rich. The present results are in generally good accord with available experimental data for quantum well systems.     

Charge and energy transfer in double asymmetric quantum wells with quantum dots

The luminescence and luminescence excitation spectra of CdSe/ZnSe quantum dots are studied in a set of double quantum wells with the ZnSe barrier of width 14 nm, the same amount of a deposited CdSe layer forming a deep well and shallow wells with different depths. It is found that for a certain relation between the depths of shallow and deep wells in this set, conditions are realized under which the exciton channel in the luminescence excitation spectrum of a shallow well dominates in the region of kinetic exciton energies exceeding 10 longitudinal optical phonons above the bottom of the exciton band of the ZnSe barrier. A model is developed for the transfer of electrons, holes, and excitons between the electronic states of shallow and deep quantum wells separated by wide enough barriers. It is shown that the most probable process of electronic energy transfer between the states of shallow and deep quantum wells is indirect tunneling with the simultaneous excitation of a longitudinal optical phonon in the lattice. Because the probability of this process for single charge carriers considerably exceeds the exciton tunneling probability, a system of double quantum wells can be prepared in which, in the case of weak enough excitation, the states of quantum dots in shallow quantum wells will be mainly populated by excitons, which explains experimental results obtained.     

Relaxation of hot excitons in CdZnSe/ZnSe quantum wells and quantum dots

The relaxation dynamics of hot excitons was studied in (Zn,Cd)Se/ZnSe quantum wells and quantum dots. A fast population of the radiative excitonic ground state occurs for an excitation excess energy corresponding to an integer number of optical phonon energies. This is indicated by a spectrally narrow photoluminescence peak observed immediately after the exciting laser pulse. Spatial diffusion of excitons, controlled by the interaction between excitons and acoustic phonons, causes a distinct linewidth broadening with increasing delay time in quantum wells. In contrast, this process is found to be strongly suppressed in quantum dots.     

Investigation of hot electrons and hot phonons generated within an AlN/GaN high electron mobility transistor

We review our recent results obtained on an AlN/GaN-based high-electron-mobility transistor. The temperature of the electrons drifting under a relatively-high electric field is significantly higher than the lattice temperature (i.e., the hot electrons are generated). These hot electrons are produced through the Fröhlich interaction between the drifting electrons and long-lived longitudinal-optical phonons. By fitting electric field vs. electron temperature deduced from the measurements of photoluminescence spectra to a theoretical model, we have deduced the longitudinal-optical-phonon emission time for each electron is to be on the order of 100 fs. We have also measured the decay time constant for LO phonons to be about 4.2 ps. An electric field present in a GaN/AlN heterostructure can bring both the first-order and second-order Raman scattering processes into strong resonances. The resonant Stokes and anti-Stokes Raman scattering results in the increase and decrease of non-equilibrium longitudinal-optical phonon temperatures, respectively. Moreover, the phonon temperature measured from the Raman scattering is increased with an applied electric field at a much higher rate than the lattice temperature due to the presence of field-induced non-equilibrium longitudinal-optical phonons.     

The theory of the cyclotron resonance line half-width in limited-size systems

Many-phonon optical transitions between Landau levels and size quantization levels in a longitudinal magnetic field are investigated in solitary quantum wells. The developed theory makes it possible to describe the intensity of the cyclotron resonance line as well as the temperature and field dependences of its half-width. The theoretical results are compared with experimental data. It is shown that when the interaction between electrons and optical phonons is taken into account, phonon satellites may appear as a result of an electron transition between the size quantization levels and magnetic levels.     

Cascade theory of electron capture in quantum wells

A cascade theory of electron capture in shallow quantum wells, when the capture process is determined by the interaction with acoustic phonons, is constructed. In these conditions, the ejection of electrons falling into a well back to the conduction band is significant. The possibility of electron ejection is taken into account by introducing an sticking probability for electrons located in the well. Such an approach is analogous to the Lax cascade theory of electron capture at small impurity centers. Calculations have been performed for wells 3 and 4 nm in width in the Al_0.05Ga_0.95As/GaAs/Al_0.05Ga_0.95As heterostructure. The developed theory has also made it possible to describe thermal ejection of electrons from shallow quantum wells.     

Influence of Nonequilibrium LO Phonons on High-frequency Performance of One-dimensional Hot Electrons in Quantum Wires of Polar Semiconductors

Small-signal ac transport of degenerate one-dimensional hot electrons in quantum wires of GaAs and In_0.53Ga_0.47As is studied for lattice temperatures of 77 K and 300 K. The carrier energy loss via polar optic phonons and momentum losses via polar optic phonons, acoustic phonons and ionized impurities are included in the calculations. Alloy disorder scattering in momentum loss is additionally incorporated for (In,Ga)As. The consideration of nonequilibrium optical phonons or hot phonons is found to enhance the 3dB cut-off frequency (f_3dB) considerably, where the ac mobility falls to 0.707 of its low frequency value. f_3dB is generally higher for (In,Ga)As quantum wire than for GaAs.     

Probing of the multilayer Si/SiGe structure with a flux of nonequilibrium acoustic phonons

The Si/Si_0.8Ge_0.2/Si double quantum wells grown on a silicon substrate were probed in the reflection geometry with a flux of terahertz nonequilibrium acoustic phonons produced by the heat pulse technique. A comparison of the detected phonon arrival signals with those obtained under similar conditions from a silicon sample without a quantum well structure permits one to isolate the component due to the phonon reflection from quantum wells. This reflected signal was found to be strongly anisotropic.     

Intraband population inversion and amplification of IR radiation through charge-carrier injection into quantum wells and quantum dots

A mechanism is proposed for obtaining intraband population inversion of electrons in size-quantization levels through the injection of electron-hole pairs into the i region of a heterostructure with quantum wells or quantum dots. Key elements of the mechanism are the simultaneous generation of interband (hv≈E _g ) near-IR radiation and the presence of a “metastable” level. In quantum wells such a level can be produced by making use of the weak overlap of the wave functions of electrons in the levels of a quantum well of complicated configuration and exploiting the characteristic features of the interaction of electrons with optical phonons in polar semiconductors. In quantum dots such a level forms as a result of the phonon bottleneck effect. Estimates are made of the gain for mid-IR radiation in intraband optical transitions of electrons. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 5, 392–399 (10 September 1998)     

Optical detection of the absorption of acoustical phonons by a two-dimensional electron gas in a magnetic field

The effect of absorption of nonequilibrium acoustical phonons on the intensity of recombination of a two-dimensional electron gas in a magnetic field is investigated. The nonequilibrium acoustical phonons are emitted in the relaxation of electrons in a tunnel junction deposited on the back side of a sample with a two-dimensional electronic channel. It is demonstrated that the optical signal showing the intensity of the recombination of nonequilibrium electrons from a photoexcited size-quantization subband can serve as a sensitive detector of acoustical phonons. Because the general heating of two-dimensional carriers and the intersubband transitions stimulated by the absorption of nonequilibrium acoustical phonons lead to effects of different sign, the useful signal can be discriminated unambiguously. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 30–35 (10 January 1999)     

Energy relaxation of magnetically confined electrons in quantum cascade lasers

By measuring the light emitted from a quantum cascade laser placed in a high magnetic field, we have investigated the energy relaxation of 0D magnetically confined electrons in the active quantum wells of the structure. The experiment consists of injecting electrons by tunnelling into one upper subband level and monitoring a resonant interaction with optical phonons produced by Landau tuning of subband energy levels. For this purpose, the upper level lifetime is probed by measuring the laser intensity as a function of magnetic field, under constant current bias values. Both the laser intensity and the bias voltage oscillate periodically with the reciprocal of the field. In addition, at high magnetic fields, the current threshold goes through deep minima at antiresonance values. The lifetime is then deduced and analyzed using the strong electron–phonon coupling scheme which is typically applied to quantum dots.     

Intersubband radiation in weakly bound superlattice structures with wide quantum wells in a transverse electric field

Long-wavelength IR radiation was detected in a long-period superlattice with wide quantum wells under conditions of electrical injection of charge carriers into lower size-quantization subbands, which was explained by intersubband transitions. The detected radiation probably suggests that there is a strongly nonequilibrium carrier distribution in subbands, caused by the difference between scattering processes into lower subbands with and without involving optical phonons.     

Ground State of a Polaron in a Symmetric Triangular Quantum Well

We study the effects of electron-phonon interaction on the electron ground state in a symmetric triangular quantum well, and calculate the ground state energy of an electron in the GaAs/Al0.96Ga0.04As triangular quantum well including the effects of the interaction between electrons and confined LO phonons by using a modified Lee-Low-Pines variational method. The electron wavefunction in the triangular well is chosen as the Airy function. The numerical results are given and discussed.